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    <title>Instance: kd</title>
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    <h1> Instance: kd </h1>
    <a href="./Instance_ kd_files/kd.jpg"><img height="200px" src="./Instance_ kd_files/kd.jpg" alt="mine picture" class="mine_image" /></a>
    <ol id="toc">
      <li id="content">Contents:</li>
      <li><a href="http://mansci-web.uai.cl/minelib/kd.xhtml#mozTocId218371">Information</a></li>
      <li><a href="http://mansci-web.uai.cl/minelib/kd.xhtml#mozTocId958846">File downloads</a></li>
      <li><a href="http://mansci-web.uai.cl/minelib/kd.xhtml#mozTocId536400">Solution files</a>
        <ol>
          <li><a href="http://mansci-web.uai.cl/minelib/kd.xhtml#mozTocId777748">UPIT</a></li>
          <li><a href="http://mansci-web.uai.cl/minelib/kd.xhtml#mozTocId341579">CPIT</a></li>
          <li><a href="http://mansci-web.uai.cl/minelib/kd.xhtml#mozTocId782032">PCPSP</a></li>
        </ol>
      </li>
      <li><a href="http://mansci-web.uai.cl/minelib/kd.xhtml#mozTocId492052">References</a></li>
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    <br />
    <h2><a id="mozTocId218371" class="mozTocH2" />Information:</h2>
    <dl>
      <dt>Description:</dt>
        <dd>Arizona’s Copper Deposit (KD)</dd>
      <dt>Block model:</dt>
        <dd>Blocks dimension: 20x20x15 m</dd>
        <dd>Precedence computed with 45 degrees using 8 levels</dd>
        <dd>Destinations: 1=ore, 2=waste</dd>
      <dt>Blockfile columns detail:</dt>
        <dd>&lt;id&gt; &lt;x&gt; &lt;y&gt; &lt;z&gt; &lt;tonn&gt;
          &lt;blockvalue&gt; &lt;destination&gt; &lt;CU %&gt;
          &lt;process_profit&gt;</dd>
      <dt>Blockvalue computation</dt>
        <dd>Profit computed using mininig cost = -0.75 per ton. <br />
          (i.e., blockvalue = -0.75 * tonn + process_profit)</dd>
        <dd>Discount rate = 0.15</dd>
      <dt>Type of Constraints:</dt>
        <dd>Process capacity of 10M tons/year and unlimited mining capacity.</dd>
    </dl>
    <h2><a id="mozTocId958846" class="mozTocH2" />File downloads:</h2>
    <ul>
      <li>.blocks file: <a href="http://mansci-web.uai.cl/minelib/data/kd.blocks">kd.blocks</a><br />
      </li>
      <li>.prec file: <a href="http://mansci-web.uai.cl/minelib/data/kd.prec">kd.prec</a></li>
      <li>.upit file: <a href="http://mansci-web.uai.cl/minelib/data/kd.upit">kd.upit</a></li>
      <li>.cpit file: <a href="http://mansci-web.uai.cl/minelib/data/kd.cpit">kd.cpit</a></li>
      <li>.pcpsp file: <a href="http://mansci-web.uai.cl/minelib/data/kd.pcpsp">kd.pcpsp</a></li>
    </ul>
    Download the <a href="http://mansci-web.uai.cl/minelib/minelib_format.pdf">Minelib data format specification</a>.
    <h2><a id="mozTocId536400" class="mozTocH2" />Solution files:</h2>
    <h3><a id="mozTocId777748" class="mozTocH3" />UPIT</h3>
    <dl>
      <dt>Download: <a href="http://mansci-web.uai.cl/minelib/sols/kd_upit.sol">kd_upit.sol</a></dt>
        <dd>Objective value: 652,195,037</dd>
        <dd>Computed using Hochbaum's pseudoflow algorithm. <a href="http://mansci-web.uai.cl/minelib/kd.xhtml#cite:hochbaumpsudoflow">[*]</a>
        </dd>
    </dl>
    <h3><a id="mozTocId341579" class="mozTocH3" />CPIT</h3>
    <dl>
      <dt>Download: <a href="http://mansci-web.uai.cl/minelib/sols/kd_cpit_gmunoz120723.sol">kd_cpit_gmunoz120723.sol</a></dt>
        <dd>Objective value: 396,858,193 (LP GAP 3.1%)</dd>
        <dd>Provided by Gonzalo Muñoz, and obtained from the LP relaxation using
          a modified TopoSort heuristic. <a href="http://mansci-web.uai.cl/minelib/kd.xhtml#cite:gmunoz_tesis">[*]</a></dd>
      <dt>Download: <a href="http://mansci-web.uai.cl/minelib/sols/kd.LPcpit">kd.LPcpit</a></dt>
        <dd>LP relaxation solution (not feasible)</dd>
        <dd>Objective value: 409,498,555</dd>
        <dd>Computed using a modified version of Bienstock &amp; Zuckerberg
          algorithm. <a href="http://mansci-web.uai.cl/minelib/kd.xhtml#cite:bzipco2010">[*]</a></dd>
    </dl>
    <h3><a id="mozTocId782032" class="mozTocH3" />PCPSP</h3>
    <dl>
      <dt>Download: <a href="http://mansci-web.uai.cl/minelib/sols/kd_pcpsp_gmunoz120723.sol">kd_pcpsp_gmunoz120723.sol</a></dt>
        <dd>Objective value: 406,871,207 (LP GAP 1.0%)</dd>
        <dd>Provided by Gonzalo Muñoz, and obtained from the LP relaxation using
          a modified TopoSort heuristic.<a href="http://mansci-web.uai.cl/minelib/kd.xhtml#cite:gmunoz_tesis">[*]</a></dd>
      <dt>Download: <a href="http://mansci-web.uai.cl/minelib/sols/kd.LPcpit">kd.LPpcpsp</a></dt>
        <dd>LP relaxation solution (not feasible)</dd>
        <dd>Objective value: 410,891,003</dd>
        <dd>Computed using a modified version of Bienstock &amp; Zuckerberg
          algorithm.<a href="http://mansci-web.uai.cl/minelib/kd.xhtml#cite:bzipco2010">[*]</a> </dd>
    </dl>
    <p />
    <h2><a id="mozTocId492052" class="mozTocH2" />References:</h2>
    <ul class="references">
      <li><a id="cite:bzipco2010" />Daniel Bienstock,
        Mark Zuckerberg (2010), Solving LP Relaxations of Large-Scale Precedence
        Constrained Problems. IPCO 2010: 1-14</li>
      <li><a id="cite:hochbaumpsudoflow" />Dorit
        S. Hochbaum (2008), The Pseudoflow Algorithm: A New Algorithm for the
        Maximum-Flow Problem. Operations Research 56(4): 992-1009<br />
      </li>
      <li><a id="cite:gmunoz_tesis" />Gonzalo Muñoz
        (2012), Modelos de optimizacion lineal entera y aplicaciones a la
        mineria. Master thesis, Dept. Mathematical Engineering, Universidad de
        Chile.<br />
      </li>
    </ul>
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